What is the value of x?sin(x+37)°=cos(2x+8)°Enter your answer in the box.x =
Accepted Solution
A:
Applying the trig formula: sin a = cos (90 - a) cos (2x + 8) = sin (x + 37) = cos (90 - x - 37) = cos (53 - x) Property of the cosine function --> ( 2 x + 8 ) = ± ( 53 − x )
a. 2x + 8 = 53 - x 3x = 45 x = 15 ∘
b. 2x + 8 = - 53 + x x = − 61 ∘
For general answers, add k 360 ∘
Check by calculator. x = 15 --> sin (x + 37) = sin 52 = 0.788 cos (2x + 8) = cos (38) = 0.788. Proved x = - 61 --> sin (x + 37) = sin (- 24) = - sin 24 = - 0.407 cos (2x + 8) = cos (-122 + 8) = cos (- 114) = - 0.407. Proved